What is the difference between ODE and scalar differential equation?

Question

Can someone please explaine what scalar diffrential equation mean? What is the difference between ODE and scalar differential equation?

Answer 1

An ODE is a differential equation consisting of one or more functions of one independent variable and their derivatives.

A scalar differential equation is a differential equation consisting of one function of one or more independent variables and their derivatives/partial derivatives.

Thus an ODE may not be scalar equation. For example: System of ODE given by \begin{eqnarray} u'(t)=f(t)\\ v'(t)=g(t) \end{eqnarray}

On the other hand a scalar equation need not be an ODE. For example : $$u_t+au_x=0$$